package com.leetcode.algorithm.y22.m06;

/**
 * 64. 最小路径和
 * 
 * https://leetcode.cn/problems/minimum-path-sum/
 * 
 * @author jie.deng
 *
 */
class Question0064Solution01 {

	public int minPathSum(int[][] grid) {
		int m = grid.length;
		int n = grid[0].length;
		// DP状态定义
		int[][] dp = new int[m][n];

		// 初始化
		dp[0][0] = grid[0][0];
		for (int i = 1; i < m; i++) {
			dp[i][0] = dp[i - 1][0] + grid[i][0];
		}
		for (int j = 1; j < n; j++) {
			dp[0][j] = dp[0][j - 1] + grid[0][j];
		}

		// 状态转移方程
		for (int i = 1; i < m; i++) {
			for (int j = 1; j < n; j++) {
				dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
			}
		}

		return dp[m - 1][n - 1];
	}

}